There is a certain problem i see with that mechanic. In that case, as soon as the Andenaj or Jewel fulfills its quota of 500 HP, i'll sell it and use another virgin Andenaj untill I gain another 500. I once made 18 Andenajs plus an Andenaj upgraded version. If you're going this direction, you must limit Branches and make Jewels a rare obtainable item instead of a shop item.
And I see a problem with your problem (Deal with it [-)). If Aero can make Andenaj to be exactly like Franscisca, then the problem you mentioned won't happen, because the system is not something connected with the item itself. What I mean is, even if you did make another Franscisca, you couldn't gain the stats over and over because the system already registered the stats you've gained and a new item would not "rewrite" it.
But of course, if Aero can't do this, the problem will exist, but your sollution sounds plausible enough to me, so... no problem
?